Obviously, at a location \(\tilde{y}\) ,
we do not want to compute all affine pieces in (REF ),
whose number is for instance given by (REF ) for \(A_n\) .
To reduce the complexity of this evaluation,
the idea is to exploit the symmetries of \(f\) 
by “folding" the function and mapping distinct regions
of the input domain to the same location.
If folding is applied sequentially, i.e. fold a region that has already been folded, the gain becomes exponential.
The notion of folding the input space in the context of neural networks
was introduced in [1]} and [2]}.
We first present the folding procedure for the lattice \(A_n\) 
and explain how this translate into a deep neural networks.
We then show that this strategy
can also be applied to the other dense lattices studied in Section REF .
